Anna Barney, Antonio De Stefano ISVR, University of Southampton, UK & Nathalie Henrich LAM, Université Paris VI, France The Effect of Glottal Opening on the Acoustic Response of the Vocal Tract

Introduction We are interested in the interaction between the voice source and the vocal tract. We hope that an improved understanding of source-tract interaction will enhance naturalness in synthesised speech

Structure of this talk Types of source-tract interaction Effect of source-tract interaction on formant frequencies: theory Mechanical model Measurement of the effect of source- tract interaction: static Measurement of the effect of source- tract interaction: dynamic Conclusions & Future work

Assumptions of Source- Filter Theory Source and vocal-tract filter do not interact Non-linear effects are normally lumped into the source model Formants are the resonances of the vocal-tract, calculated when the glottal impedance is infinite

Source Tract Interaction (STI) Childers & Wong (1994) define 3 principal types of STI: Loading of the source by the vocal tract impedance Dissipation of vocal tract energy by glottal opening (mainly at F1) Carry over of energy from one glottal period to the next (for low glottal damping) (D.G. Childers and C.-F. Wong, 'Measuring and Modeling Vocal Source-Tract Interaction', IEEE Transactions on Biomedical Engineering, Vol. 41. No. 7. pp (1994) )

Source Tract Interaction (STI) Flanagan (Speech analysis synthesis and perception, 1965) considered the effect of finite glottal impedance on a transmission line model of the vocal tract ZaZa ZaZa ZbZb ZaZa ZaZa ZbZb ZgZg ZlZl supraglottal vocal tract Subglottal vocal tract glottis ZoZo

Source Tract Interaction (STI) Flanagan stated that a finite glottal impedance would raise F1 and increase formant damping He predicted and increase in F1 of 1.4% for a glottal area of 5 mm 2

Source Tract Interaction (STI) Ananthapadmanabha, T.V. & Fant G. (1982) (Calculation of the true glottal volume velocity and its components. Speech Commun. 1 (1982) ). Found the theoretical effect of glottal inertance to be small

Source Tract Interaction (STI) P. Badin and G. Fant, (Notes on Vocal tract computation. STL-QPSR 2-3/1984 (1984) ) Modelled the sub-glottal system as a short circuit used a glottal area of mm 2, glottis modelled by inductance only: F1 increased by 0.2%

Measurements on Real Speech It is known that the formant estimates vary depending on where in a pitch period the estimation window is placed. F1 estimated during open phase using group delay characteristics and a minimum phase assumption are generally a little higher during open phase than during closed phase. (B Yeganarayana, R Veldhuis IEEE trans speech & audio processing, 6(4) 1998) Closed-phase formant analysis is used to get estimates of the vocal tract formants that are reliably decoupled from any sub- glottal formants. (L.C.Wood, D.J.P Pearce IEE Proceedings 136 pt 1 no )

Source Tract Interaction (STI) Shifts in F1 may be small but they may correlate with: – changes in glottal OQ and/or –changes in glottal amplitude And may be of interest when considering voice quality & naturalness of synthesis Also – glottal areas considered in the literature are always at the small end of the range found in normal voicing.

Flanagan’s model We implemented Flanagan’s transmission line model with a uniform duct of length 17.5 cm and area 2.89 cm 2 to explore the change as glottal width increased

The formant shift – theory Frequency (Hz) Log amplitude

Theoretical modelling of the formant shift – static glottis To match our experimental measurements we elaborated on Flanagan’s model We used 4 T-sections for the supra-glottal vocal tract and other parameters to match those of our mechanical model We chose the boundary condition at the lips to match the boundary condition for our measurements

Theoretical modelling of the formant shift –glottal impedance model Flanagan (1965) & others for finite glottal impedance:

Theoretical modelling of– glottal impedance model Laine & Karjalainen (1986): where

Theoretical modelling of the formant shift –glottal impedance model Rösler & Strube (1989) Where

Theoretical modelling of the formant shift –glottal impedance model How should we model the sub- glottal impedance? Speech models often assume that the lower end of the trachea is a fully absorbing boundary (r=0) so that there are no sub- glottal resonances.

Theoretical modelling of the formant shift –glottal impedance model We wanted to compare our theoretical model with measurements. We tried all three glottal impedance models and a range of sub-glottal impedance models to find the best fit to the data.

The Mechanical Model We made our measurements of F1 shift using a mechanical model of the larynx and vocal tract

The mechanical model

Shutter Driver System The shutter region

Schematic Diagram of the Model pt1 pt2 pt flow All dimensions in mm, not to scale

Instrumentation  Rotameter -Inlet volume flow rate  Manometer -Mean pressure upstream  Entran EPE-54 miniature pressure transducers, diameter of 2.36 mm, range 0 to 14kPa -Time-varying pressure at the duct wall for up to 4 locations.  Shutter driving signal - shutter position  All time-histories are captured by a simultaneous-sampling ADC connected to a PC with a sampling frequency of 8928 Hz.

Experimental measurements – static case Glottal widths of 0,1,2,3 mm Excitation provided by speaker at duct outlet – tonal discrete frequencies between 300 Hz and 2 kHz Speaker modified duct boundary condition at “lips” so it was closer to a closed end condition. Impedance here was held constant throughout the measurements

Experimental measurements – static case 2 pressure transducers between “glottis” and “lips” Pressure transducer separation 80 mm Standing wave component pressure amplitudes extracted as specified by K R Holland & POAL Davies (The measurement of sound power flux in flow ducts. Journal of Sound and Vibration 230 (2000) ) Transfer function from “glottis” to “lips” obtained.

Transfer function from glottis to lips – measured & theoretical - static dB

Transfer function from glottis to lips – measured & theoretical - static dB

Transfer function from glottis to lips – measured & theoretical - static dB

Transfer function from glottis to lips – measured & theoretical - static dB

Glottal width Flanagan model, Flanagan factor of 6/5 L & K model R & S model 1 mm MSE mm MSE mm MSE

dB 0 mm 1 mm 2 mm 3 mm

Static case - Summary F1 & F2 increased with increasing glottal width Predicted values of F1 (799 Hz, 854 Hz, 882 Hz, 896 Hz) match well to measurements Increase in F1 between closed glottis and 1 mm wide glottis is ~6% Increase in F1 between closed glottis and 3 mm wide glottis is ~13% Increase in F1 larger than found by previous researchers, perhaps due to using greater glottal widths

Dynamic Experimental measurements How do our measurements for the static case transfer to a model excited by a vibrating larynx? What is the dependence of F1 on the open quotient? What is the dependence of F1 on the glottal amplitude?

Experimental measurements – dynamic Moving shutters 10 – 40 Hz square wave excitation OQ: 20, 40, 60, 80 % Glottal width: 0.25 mm to 4 mm

Peak glottal width versus OQ for all f Open quotient Glottal amplitude

Pressure time history at p1 in the duct Time (s) Pressure (Pa) closure opening

Experimental measurements – dynamic F1 frequency found from AR spectral estimation. AR analysis uses whole glottal cycle to ensure STI effects included in analysis AR analysis uses the Yule-Walker algorithm with an order of ceil((Fs/1000)+2) = 11

Experimental measurements – dynamic F1 peak defined as maximum value of spectrum between 200 Hz and 1 kHz Data set rejected if no peak visible in this range hence small data set for OQ = 80%

AR analysis

Frequency of F1 for changing glottal width and OQ Glottal width (mm) F1 (Hz)

Summary – dynamic measurements F1 increases with increasing glottal width for fixed OQ F1 increases with increasing OQ for fixed glottal width – at least at small glottal widths Observed values of F1 much higher than normally predicted for open-closed tube of the same length or expected for real speech.

Theoretical model – dynamic Simulink model Model adapted from one created by Nicolas Montgermont and Benoit Fabre, LAM for investigating the flute

Duct model Switchable glottal impedance Glottal excitation Simulink model of dynamic case

Pressure time history at P1 - simulated open closed

F1 values for dynamic simulation

Simulation - summary The simulation does show a change in the formant frequency as OQ changes The increase in F1 is much smaller than observed in the dynamic model experiments The dynamic model has much greater damping, especially during closure, than the simulation

Future work To make a theoretical model of the formant shift in the dynamic case that matches the measurements more closely To make similar measurements in real speakers